X₅₉₀

ISOGONAL CONJUGATE OF X₅₈₈

X₅₉₀ is the isogonal conjugate of X₅₈₈.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₅₉₀ (ISOGONAL CONJUGATE OF X₅₈₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Medial Triangle △M_aM_bM_c — vertices M_a, M_b, M_c (Formed by the midpoints of sides BC, CA, AB)

• Central Lines: {2, 492}

• Related Centers: X₂ (CENTROID), X₄₉₂ (CEVAPOINT OF X₂ AND X₄₈₈)

Trilinears: \((a^{2} + 4 \operatorname{area}(ABC))/a : :\)

Barycentrics: \(a^{2}\) + 2S : : X₅₉₀ lies on these lines: 1,3302 2,6 3,485 4,1151 5,371 11,2066 12,2067 17,3389 32,640 39,642 53,1585 140,372 157,3155 393,3535 397,2045 398,2046 486,1656 493,2165 498,1335 499,1124 588,2963 605,748 606,750 631,1152 639,1504 1131,3522 1327,3534 1578,3546 1579,3547 1583,1609 1588,3090 1834,2047 3085,3298 3086,3297 3087,3536 3092,3542 3093,3541 3312,3526 3525,3594

Search Value (6, 9, 13): \(1.808227078519\)

▸ Alternate Coordinates2 forms

• Trilinears: \(\sin A + 2 \sin B \sin C : :\)

• Trilinears: \(aR + bc : :\)

▸ Functional Relations9 relations

• X₅₉₀ = isogonal conjugate of X₅₈₈

• X₅₉₀ = complement of X₄₉₂

• X₅₉₀ = crosspoint of X₂ and X₄₈₅

• X₅₉₀ = crosssum of X₆ and X₃₇₁

• X₅₉₀ = perspector of circumconic centered at X₆₄₁

• X₅₉₀ = center of circumconic that is locus of trilinear poles of lines passing through X₆₄₁

• X₅₉₀ = X₂-Ceva conjugate of X₆₄₁

• X₅₉₀ = homothetic center of outer Vecten and 3rd tri-squares triangles

• X₅₉₀ = homothetic center of [outer Vecten of outer Vecten triangle] and pedal triangle of X₁₁₅₁